In　this　paper,　an　in-motion　initial　alignment　algorithm　based　on　Lie　group　is　proposed,　which　effectively　solves　the　non-uniqueness　of　the　unit-quaternion　attitude　description　and　the　nonlinear　problem　when　using　unit-quaternion　for　state　estimation.　The　algorithm　divides　the　attitude　matrix　into　three　successive　special　orthogonal　matrices　according　to　the　property　of　the　rotation　on　Lie　group　description　and　the　basic　principle　of　inertial　navigation,　and　isolates　the　angular　velocity　and　linear　velocity　of　the　carrier　under　dynamic　conditions.　Based　on　the　mapping　relation　between　Lie　group　and　Lie　algebra　and　the　optimal　estimation　principle,　and　the　uncertainty　of　measurement　noise　in　modeling　is　analyzed,　an　adaptive　Lie　group　filter　method　is　proposed　to　estimate　the　initial　inertial　matrix　directly.　It　can　be　seen　from　the　experimental　results　that　compare　with　the　unit　quaternion　algorithm　proposed　algorithm　has　improved　the　alignment　accuracy　and　stability.　This　method　is　an　excellent　situation　to　the　SINS　initial　alignment　in-motion.